Targeted suppression of failure spreading in multistable oscillator networks

Abstract

Fluctuations and damages crucially determine the operation and stability of networked systems across disciplines, from electrical powergrids, to vascular networks or neuronal networks. Local changes in the underlying dynamics may affect the whole network and, in the worst case, cause a total collapse of the system through a cascading failure. It has been demonstrated that certain subgraphs can reduce failure spreading drastically, or even inhibit it completely. However, this shielding effect is poorly understood for non-linear dynamical models. Here, we study the effect of perturbations in networks of oscillators coupled via the Kuramoto model. We demonstrate how the network structure can be optimised for suppressing specific, targeted fluctuations at a desired operational state while letting others pass. We illustrate our approach by demonstrating that a significant reduction in time-dependent fluctuations may be achieved by optimising the edge weights. Finally, we demonstrate how to apply the developed method to real-world supply networks such as power grids. Our findings reveal that a targeted shielding of specific solutions in multistable systems is possible which may be applied to make supply networks more robust.